The research of Anders and Per Martin-Löf has influenced statistical theory, especially concerning exponential families, the expectation–maximization method for missing data, and model selection.

Martin-Löf's first paper discussed the problem of estimating the mortality rates of the Dunlin species, using capture-recapture methods.

The problem of determining the biological sex of a bird, which is extremely difficult for humans, is one of the first examples in Martin-Löf's lectures on statistical models.

Martin-Löf wrote a licenciate thesis on probability on algebraic structures, particularly semigroups, while a student of Ulf Grenander at Stockholm University.

In his paper "On Tables of Random Numbers", Kolmogorov observed that the frequency probability notion of the limiting properties of infinite sequences failed to provide a foundation for statistics, which considers only finite samples.

In the 1970s, Per Martin-Löf made important contributions to statistical theory and inspired further research, especially by Scandinavian statisticians including Rolf Sundberg, Thomas Höglund, and Steffan Lauritzen.

In this work, Martin-Löf's previous research on probability measures on semigroups led to a notion of "repetitive structure" and a novel treatment of sufficient statistics, in which one-parameter exponential families were characterized.

He has been interested in Central-European philosophical traditions, especially of the German-language writings of Franz Brentano, Gottlob Frege, and of Edmund Husserl.

From 1968 to '69 he worked as an assistant professor at the University of Chicago where he met William Alvin Howard with whom he discussed issues related to the Curry–Howard correspondence.

A number of popular computer-based proof systems are based on type theory, for example NuPRL, LEGO, Coq, ALF, Agda, Twelf, Epigram, and Idris.